航空学报 > 2003, Vol. 24 Issue (4): 328-331

用图论方法分析马尔可夫频次阵特性

陈志伟1, 高海龙2, 王智1   

  1. 1. 北京航空工程研究中心, 北京9203 信箱, 北京 100076;2. 空军工程大学工程学院, 陕西西安 710038
  • 收稿日期:2002-06-25 修回日期:2003-04-23 出版日期:2003-08-25 发布日期:2003-08-25

Analyzing Characteristics of Markov Frequency Matrix Using Graph Theory

CHEN Zhi-wei1, GAO Hai-long2, WANG Zhi1   

  1. 1. Beijing Aeronautical Technology Research Center; Beijing 100076; China;2. Engineering Institute; Air Force Engineering University; Xi'an 710038; China
  • Received:2002-06-25 Revised:2003-04-23 Online:2003-08-25 Published:2003-08-25

摘要: 简述了飞机机动疲劳载荷谱的各种常用表征方法及其优点与不足, 重点论述疲劳载荷状态转移的马尔可夫频次矩阵法。结合示例说明马尔可夫频次阵的构造形成与计算机编程填充方法。利用图论研究方法说明马尔可夫阵是一幅欧拉图的邻接矩阵, 阐述了其重要特性, 给出了据此构造疲劳载荷历程的要求与做法,并给出了数据处理实例。通过讨论马尔可夫阵与其他疲劳载荷表征方法间的关系, 表明马尔可夫矩阵含有更多信息, 是较适合完整描述疲劳载荷谱的表征方法之一。

关键词: 疲劳载荷, 载荷历程, 马尔可夫矩阵, 图论, 邻接矩阵, 欧拉图

Abstract: After briefing the merits and demerits of some commonly used methods to char acterize air craft maneuverfatigue loads, the Markov frequency matrix is examined in the view to describe load state transition events. Theform and construction of the Markov matrix are illustrated by an example, and the method to fill the matrix by computer programming is explained. According to the graph theory, the Markov matr ix is re-examined as the adjacentmatrix of weighted multiple directional graphs with Euler ian loop. The features of Markov frequency matr ix and ther equirements for a matrix to r ealize fatigue load history construct ion are outlined, and an example of processing datafor an aircraft flight mission was presented. Discussions showed Mar kov matrix characterization has more useful information than other forms have and is yet easily transformed into other forms.

Key words: fatigue load, load history, Markov matrix, graph theory, adjacent matrix, Eulerian graph

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